Ratemaking 保险费率厘定

1. Ratemaking 保险费率厘定 Steve D’Arcy 史蒂夫·达尔希 Chairman of the Board of the Casualty Actuarial Society 财险精算协会董事会主席 Professor of Finance at the University of Illinois 伊利诺伊大学金融学教授 Presented at Nankai University 南开大学 June 29, 2006

2. Overview 提纲 • Objectives in Ratemaking保险费率厘定的目标 • Terminology术语 • Ratemaking Methods 保险费率厘定方法 • Advanced Issues 高级问题讨论 • Sources for Additional Information 补充信息资源

3. Ratemaking Objectives for Companies公司保险费率厘定的目标 Rates should be: 费率应该： Stable 稳定 Responsive 合理 Promote loss control 促进防损 Cover contingencies 包括意外损失 Understandable 被理解、接受

4. Other Ratemaking Objectives其它保险费率厘定目标 Regulatory view (in United States) 从法规角度看（美国） Rates must be: 费率必须 Adequate 充足 Not excessive 不过高 Not unfairly discriminatory 不能不公平的加以区别 Financial market view从金融市场角度看 Competitive markets will assure appropriate rates 竞争的市场将会保证恰当的费率

5. Terminology – 1 术语 Exposure unit = basic rating unit 保险金额单位=基本费率单位 Example: car year Written exposures 投保的保险金额 Exposures on policies written during period 在保险合同期内的被保金额 Earned exposures 以获保的保险金额 Exposure units actually exposed to loss during period 在保险合同期内实际已经承担损失的保险金额 Example A policy covering 2 cars is written on October 1, 2006 一份保险单投保2辆汽车 Written exposure for 2006 = 2 car years Earned exposure for 2006 = 2 x ¼ of a year = ½ car years

6. Terminology - 2 Written premium 保险费 Premiums booked 以入账的保险费 Earned premium 满期保险费 Pro-rata portion of premiums exposed to loss 按实际承担损失比例均摊的保险费 Claim frequency 索赔频率 Number of claims per exposure unit 每保险金额单位索赔的数量 Severity 索赔额度 Average loss per claim 每次索赔的平均赔付额 Pure premium 纯保险费 Claim frequency x severity 索赔频率乘以索赔额度

7. Terminology - 3 Loss ratio: 损失率 Incurred losses plus loss adjustment expenses Earned premium （发生的损失 + 损失调整费用）/ 满期保险费 Expense ratio: 费用比率 （费用 / 总保险费） Expenses Written premium Surplus: 盈余 Assets – Liabilities 资产 – 负债

8. Terminology - 4 Combined ratio 联合损失率 Loss ratio + Expense ratio 损失率 + 费用比率 Underwriting profit margin (UPM) 承保利率 1 – Combined ratio 1 – 联合损失率 Operating ratio 经营比率 Combined ratio – investment income/earned premium 联合损失率 – 投资收益/满期保险费 What should be included in investment income 什么应该包括在投资收益中 Net investment income (interest, dividends and rents) 净投资收益（利息，分红和租金） Capital gains 资本收益 Realized or unrealized 实现的或未实现的

9. Ratemaking in the Real World保险费率厘定实际应用 Incurred losses已发生的损失 Loss reserves 损失准备金 Loss development factors 损失发展因素 Inflation 通货膨胀 Other time dependent factors (auto insurance) 其它受时间影响的因素（机动车辆保险） Traffic density 交通拥挤度 Law enforcement efforts 法律执行力度 Legal rules governing loss settlements 陪付结算的法律条例 Trending adjusts for time dependent factors 对受时间影响的因素进行趋势调整 Severity 额度 Frequency 频率

10. Ratemaking Methods 保险费率厘定的方法 Loss ratio method 损失率方法 Percent rate change = (A-E)/E 百分率变化 A = Actual loss ratio 实际损失率 E = Expected loss ratio 期望损失率 = 1 – Expense Ratio – Underwriting Profit Margin 1 – 费用比率 – 承保利率 Pure premium method 纯保险费方法 G = (P+F)/(1-V) G = Gross premium 保险费总额 P = Pure premium = frequency x severity 纯保险费 F = Fixed expenses 固定费用 V = Variable expenses (and profit) 可变费用（利润）

11. Loss Ratio Method Actual LR = 66% Expected LR = 60% Percent rate change = (66-60)/60 = +10% Pure Premium Method Pure premium = 400 Fixed expenses = 50 Variable expenses = 25% Gross premium = (400+50)/(1-.25) = 600 Examples

12. Methods for Determining the Appropriate Profit Margin – 1确定恰当利润率的方法 Standard Underwriting Profit Margin 标准承保利润率 5% (or some other constant) （或其它常数） Ignores investment income 忽略投资收益 Ignores leverage (Premium/Surplus ratio) 忽略（保险费/盈余）比率 Standard Profit Margin minus Investment Income 标准承保利润率减去投资收益 What should be included in investment income 什么应该包括在投资收益中 Net investment income (interest, dividends and rents) 净投资收益（利息，分红和租金） Capital gains 资本收益 Realized or unrealized 实现的或未实现的

13. Methods for Determining the Appropriate Profit Margin - 2 Capital Asset Pricing Model (CAPM)资本定价模型 Basic model without taxes: 不包括税收的基本模型 UPM = -k Rf + u [E(Rm) - Rf] k = funds generating coefficient 基金产生系数 Rf = risk free rate 无风险利率 E(Rm) = Expected return on market portfolio 平均市场组合期望收益率 u = underwriting beta 保险业相对市场的beta值 No compensation for underwriting risk uncorrelated with market risk 没有考虑与市场风险不相关联的承保风险

14. Methods for Determining the Appropriate Profit Margin - 3 Total Rate of Return Model 总回报率模型 TRR = (IA/S)(IR) + (P/S)(UPM) TRR = Target total rate of return 目标回报率 IA = Investable assets 可投资资产 S = Surplus 盈余 IR = Investment return 投资回报 P = Premium 保险费 UPM = Underwriting profit margin 承保利率 How is target rate of return determined? 怎样确定目标回报率

15. Methods for Determining the Appropriate Profit Margin - 4 Discounted Cash Flow Model 折现现金流模型 Equates premiums with risk adjusted cash flows for expenses, taxes and losses 经过风险调整的现金流保费收入等于支出（费用、税和损失） Need to keep track of timing of payments 需要跟踪支付的时间 No consensus on method to determine risk adjustment 没有统一的确定风险调整的方法 Allocation and timing of surplus flows is arbitrary 盈余的分配和时间的确定是主观臆断的

16. General Risk-Adjusted Discount Technique Formula PV (P) = PV (L) + PV (E) + PV (TUW) + PV (TII) where: PV = present value operator 折现指数 P = premiums 保险费 L = losses and loss adjustment expense 损失和损失调整费用 E = underwriting expenses 承保费用 TUW = taxes on underwriting profit or loss 承保利润税金 TII = taxes on investment income 投资收益税金

17. Risk Classification 风险分类 For automobile insurance 机动车辆保险 Age of driver 驾驶员年龄 Sex and marital status of driver驾驶员性别和婚姻状况 Type of vehicle 车辆类型 Use of vehicle 车辆用途 Driving record of driver 驾驶员驾驶记录 Mileage driven 行驶里程 Territory where vehicle is garaged 车辆停靠地点 Other driver characteristics – use of predictive modeling 其它关于驾驶员的特征可由预测模型得到

18. Additional Sources 补充的资料来源 Chapter 3 – Ratemaking by Charles McClenahan in the Foundations of Casualty Actuarial Science Can purchase at: http://www.casact.org/pubs/castext.htm Casualty Actuarial Society Ratemaking Seminar handouts http://www.casact.org/coneduc/ratesem/2006/handouts/ A Comparison of Property/Casualty Insurance Financial Pricing Models by D’Arcy and Gorvett http://www.casact.org/pubs/proceed/proceed98/980001.pdf Ratemaking: A Financial Economics Approach by D’Arcy and Dyer http://www.casact.org/pubs/proceed/proceed97/97301.pdf